Isothermal Thermogravimetric Study for Determining Sublimation

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Isothermal Thermogravimetric Study for Determining Sublimation Enthalpies of Some Hydroxyflavones Henoc Flores,† Fernando Ramos,† Elsa A. Camarillo,*,† Omar Santiago,† Gastón Perdomo,† Rafael Notario,‡ and Sandra Cabrera† †

Facultad de Ciencias Químicas, Benemérita Universidad Autónoma de Puebla 14 sur y Av. San Claudio, C.P. 72570, Puebla Pue, México ‡ Instituto de Química Física “Rocasolano”, CSIC, Serrano 119 28006, Madrid, España S Supporting Information *

ABSTRACT: The sublimation enthalpies of some hydroxyflavones and one amineflavone were determined with a thermogravimetric device under isothermal conditions. These enthalpies were obtained by measuring the rate of mass loss as a function of temperature. In this methodology, the Clausius−Clapeyron and Langmuir equations were used. The diffusional effect of the gas phase was included in the Langmuir equation. In order to test and validate the experimental methodology, the sublimation enthalpy of three standard materials, anthracene, pyrene, and benzoic acid, were determined. The values obtained are in agreement with the data reported and recommended in the literature. Low uncertainties were obtained in all thermogravimetric measurements. Additionally, by differential scanning calorimetry, the molar fraction, temperature and enthalpy of fusion, and heat capacity of the solid phase were determined for all of the compounds studied. The heat capacities of the gas phase were estimated using computational methods. Isothermal thermogravimetry was applied to study a family of flavones.

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INTRODUCTION The experimental determination of the enthalpies of sublimation is of paramount importance in thermochemistry because the values are necessary to obtain the enthalpy of formation of the gas phase of a compound. Furthermore, the enthalpies of sublimation provide information about the intermolecular interactions of the crystalline phase. The known methods currently used to determine the enthalpies of sublimation are classified into two groups, namely, direct and indirect. In the first group, the sublimation enthalpy is determined directly at a fixed temperature. Among this group are, for example, the vacuum sublimation drop-microcalorimetry1−3 and Calvet microcalorimetry.4−6 The indirect group includes techniques in which the temperature dependence of the vapor pressure (or some other parameter proportional to it) is measured, and here the Clausius−Clapeyron equation is used. The effusion method is the most commonly used indirect method.7−12 Thermogravimetry is another indirect method which has become a technique widely used for determining enthalpies of sublimation or the vaporization of organic compounds.13−19 In thermogravimetry, mass loss is measured as a function of temperature under dynamic or isothermal conditions. Recently our research group reported the sublimation enthalpies of methyl- and phenyl-substituted hydantoins by thermogravimetry under dynamic conditions.20 On the other hand, it has been found that in some cases it is not possible to use © XXXX American Chemical Society

thermogravimetry under dynamic conditions to determine enthalpies of sublimation. This is because many solid organic compounds have very low vapor pressures and exhibit very strong intermolecular interactions. In these experiments, mass loss cannot be recorded at temperatures below the melting temperature of the compounds when they are subjected to a heating ramp. In the case of some liquids, it is not possible to record the loss of mass as a function of temperature when determining their enthalpy of vaporization because liquid decomposition can occur when it is heated. Given this experimental difficulty, in this work we propose the use of thermogravimetry under isothermal conditions to measure the mass loss in temperature ranges that are below the melting temperature to determine the enthalpy of sublimation. In order to validate and test the isothermal methodology, three reference materials for sublimation enthalpy21 were used. Two of these are primary, anthracene and benzoic acid, and one is secondary, pyrene. The results were compared to the data reported in the literature. After this methodology was tested, it was applied to determine the sublimation enthalpies of some flavones, 3-, 5-, 6-, and 7-hydroxyflavone as well as the 6-aminoflavone. This family was selected because it is desired to analyze the influence of the hydroxy and amino groups Received: November 28, 2017 Accepted: April 19, 2018

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DOI: 10.1021/acs.jced.7b01034 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Molecular structure of the flavones studied in the present work.

Table 1. Chemical Data, Molar Mass, and Mole Fraction of the Substances Used in the Present Work chemical name

CAS number

pyrene anthracene benzoic acid 3-hydroxyflavone 5-hydroxyflavone 6-hydroxyflavone 7-hydroxyflavone 6-aminoflavone

129-00-0 120-12-7 65-85-0 577-85-5 491-78-1 6665-83-4 6665-86-7 4613-53-0

M

a

g·mol−1

202.251 178.229 122.121 238.237 238.237 238.237 238.237 237.252

supplier

initial mole fraction purity

purification method

final mole fraction purityb

analysis method

Aldrich Aldrich NIST 39 j Aldrich Aldrich Aldrich Aldrich Aldrich

0.98 >0.99 >0.99 ≥0.98 ≥0.97 0.98 ≥0.98 0.97

sublimation sublimation none crystallization crystallization crystallization crystallization crystallization

0.9992 ± 0.0003 0.9988 ± 0.0004 0.9999 ± 0.0001 0.9997 ± 0.0001 0.9999 ± 0.0001 0.9997 ± 0.0001 0.9991 ± 0.0001 0.9998 ± 0.0001

DSC DSC DSC DSC DSC DSC DSC DSC

a

Molar masses computed from the atomic weights recommended by IUPAC (2013).33 bExpanded uncertainty with coverage factor k = 1.96 and a confidence level of 0.95.

In spite of the hydroxyflavones’ importance and applications, there are no data on the thermodynamic properties, such as enthalpies of sublimation and fusion and the calorific capacities, as reported in the specialized literature. Only Sousa et al.30 have reported the sublimation enthalpy of flavone and flavanone determined by Calvet microcalorimetry.

on the sublimation enthalpy data. The results obtained are discussed and are associated with intermolecular interactions of the crystalline phase of flavones. Figure 1 shows the structure of the flavones studied in this work. The flavonoids are of the phenolic type, and they have a common diphenyl-pyran skeleton. They are characterized by having two phenyl rings joined by a pyran ring. Flavonoids are a broad group of phenolic compounds distributed in the plant kingdom. They are found universally in vascular plants and in a wide variety of fruits, vegetables, and beverages such as tea, coffee, beer, and wine. They are important compounds involved in the development and proper functioning of plants, as they act as attractants of animals during oviposition. They act as protective agents in plants against UV light and against phytopathogenic organism infections.22−24 They fulfill various functions such as the pigmentation of flowers and protection against microorganisms and arthropods and are of interest to nutritionists and pharmacologists.25,26 All flavonoids have biological activity, which has been studied since the 1930s. Hydroxyflavones are a type of flavonoids characterized by showing a variety of the number and position of the hydroxyl group. In particular, hydroxy-substituted flavones play an important role in the protection against oxidative damage phenomena, and they have therapeutic effects in a large number of pathologies, including ischemic heart disease, atherosclerosis, and cancer.27−29 Their antioxidant activity stems from the redox properties of the hydroxyphenolic groups and the relationship between the different parts of their chemical structure.

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EXPERIMENTAL METHODS Materials and Sample Preparation. The reference materials and flavones were obtained from Sigma-Aldrich Co., except the benzoic acid, which was purchased from NIST. Pyrene and anthracene were purified by sublimation under reduced pressure and subsequently stored under a nitrogen atmosphere. The flavones were purified by recrystallization from HPLC-grade ethanol, and afterward the obtained crystals were triturated and dried at 323.15 K in an oven for 24 h in order to remove any trace of solvent and were stored at 298 K under a nitrogen atmosphere. The purity of all samples was verified by DSC using TA Instruments Q2000 equipment and applying the fractional melting method and the van’t Hoff equation.31,32 Additionally, the melting temperature was calculated from the intercept of this equation, and the melting enthalpy was calculated from the area under the melting curve. To determine the molar fraction, 1 K·min−1 heating ramps were used over a range of 10 K before and after the melting temperature. All experiments performed on the DSC equipment were run under a nitrogen atmosphere of 50 cm3·min−1, and the sample masses were 1−3 mg, which were weighed in sealed cells. Prior to the experiments, the equipment was B



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calibrated for heat flow and temperature using metallic indium (x = 0.99999) as a standard material.21 Table 1 shows the molar mass and the molar fraction before and after the purification process. DSC curves for anthracene and benzoic acid are shown in the Supporting Information. Heat Capacity Measurements. The heat capacities of the crystalline phases of all samples were determined with PerkinElmer DSC 8000 equipment. The two-step method34 was used, and a synthetic sapphire sample was used as a reference material. The heating method used for the sapphire and the samples consisted of an isotherm at 293.15 K for 1 min, followed by heating from 293.15 to 10 K before the melting temperature at a rate of 10 K·min−1 and finally a 1 min isotherm at this temperature. The complete details of this technique have been previously published.20 In each experiment, a nitrogen flow of 50 cm3·min−1 was used. Approximately 5 mg of sample was placed in a hermetically sealed aluminum cell, which was weighed using a Mettler Toledo UMX2 balance (0.1 μg accuracy). In order to test this methodology, the heat capacity of the sapphire was measured at (298.15, 350, and 400) K. The values obtained were (79.02, 88.23, and 97.07) J·mol−1·K−1, respectively, which are in agreement with the values reported in the literature, (79.01, 88.84, and 96.08) J·mol−1·K−1, respectively.21 Isothermal Thermogravimetry. The determination of the sublimation enthalpies by thermogravimetry is based on the Langmuir equation, which is strictly valid only under vacuum conditions. This was modified by Pieterse and Focke in order to account for the diffusional effects of the gas phase, rendering eq 1 to be valid for measurements of mass loss under isothermal conditions.35

Table 2. Data Obtained in the Present Study and Its Comparison with Those Obtained from the Literature (p = 0.1 MPa)a Tfus K

Δlcr Hm(Tfus)

488.97 489.4 491.98 NA 489.7 ± 0.5b 422.37 ± 0.36 423.81 NA 422.7 423.9 ± 0.7b 395.5 395.50 ± 0.02 395.5 395.52 395.3 ± 0.3b 443.15−445.15 442.15−445.15 442.15−444.15 443.6 ± 0.4b 431.15−433.15 430.15 428.15−429.15 431.0 ± 0.3b 512.15 508.7−509.7 506.15−507.15 509.3 ± 0.4b 519.15−520.15 517.15 514−516.15 515.3 ± 1.1 473.15−474.15 471.9 ± 0.3b

29.37 28.8 ± 0.29 29.84 ± 0.45 29.4 ± 0.1 30.66 ± 1.54b 16.68 ± 0.54 17.36 ± 0.01 17.11 ± 0.38 17.313 17.36 ± 0.52b 17.1 18.063 ± 0.042 17.99 18.00 18.56 ± 0.49b NA NA NA 32.45 ± 1.05b NA NA NA 27.16 ± 0.69b NA NA NA 32.41 ± 1.18b NA NA NA 31.20 ± 1.08 NA 30.40 ± 0.86b

compound antracene

pyrene

benzoic acid

3-hydroxyflavone

5-hydroxyflavone

6-hydroxyflavone

7-hydroxyflavone

6-aminoflavone

reference

kJ·mol−1

37 38 39 40 this work 39 41 42 43 this work 44 21 45 46 this work 47 48 49 this work 50 51 52 this work 53 47 54 this work 55 47 56 this work 57 this work

⎛ MS ⎞ dm ⎟D = p⎜ ⎝ RT ⎠ dt

(1)

In eq 1, dm/dt is the mass loss rate, p is the vapor pressure of the compound at temperature T, M is the molar mass, R is the gas constant, D is the diffusional coefficient, and S is a characteristic factor related to the geometry of the cell containing the sample. Combining eq 1 with the integrated Clausius−Clapeyron eq 2 yields eq 3

a Standard uncertainty u(p) = 1 kPa. bExpanded uncertainty with a 0.95 confidence level and a coverage factor of k = 1.96. NA: Not available.

ln p = c −

g Δcr,1 Hm 1 R T

(2)

Table 3. Heat Capacities of Solid and Gas Phases at Constant Pressure of the Compounds Studied in the Present Work (p = 0.1 MPa)a,b anthracene Cpm(cr) c

pyrene Cpm(g)

Cpm(cr) d

benzoic acid Cpm(g)

Cpm(cr) e

3-hyroxyflavone Cpm(g)

Cpm(cr) f

Cpm(g)

T K

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

205.7 209.9 213.9 217.6 221.7 225.4 229.6 234.2 237.9 242.2 246.5 250.7 254.9 258.8 262.9

183.0 186.4 189.9 193.3 196.7 200.1 203.5 206.8 210.2 213.5 216.8 220.0 223.3 226.5 229.7

221.9 225.8 230.2 234.3 238.7 243.0 247.5 252.6 258.1 263.6 268.9 274.1 279.8 285.4 291.4

199.6 203.5 207.3 211.1 214.8 218.6 222.3 226.0 229.7 233.4 237.0 240.6 244.2 247.7 251.3

143.2 145.2 147.5 149.6 151.4 153.0 155.4 157.8 160.0 162.2 164.4 166.6 169.1 171.7 174.4

125.6 127.6 129.6 131.5 133.5 135.5 137.4 139.3 141.2 143.2 145.0 146.9 148.8 150.6 152.5

268.9 270.1 272.8 275.3 278.3 280.8 284.2 287.6 291.5 295.2 298.9 303.2 306.8 310.8 315.0

238.2 242.2 246.2 250.1 254.0 257.9 261.7 265.6 269.4 273.2 276.9 280.6 284.3 288.0 291.6

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Table 3. continued anthracene T K

368.15 373.15 378.15 383.15 388.15 393.15 398.15 403.15 408.15 413.15 418.15 423.15 428.15 433.15 438.15

Cpm(cr) c

pyrene Cpm(g)

Cpm(cr) d

benzoic acid Cpm(g)

Cpm(cr) e

3-hyroxyflavone Cpm(g)

Cpm(cr) f

Cpm(g)

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

266.9 270.6 275.2 279.2 283.2 286.9 291.7 295.8 299.3 303.3 306.8 309.9 313.4 317.4

232.8 236.0 239.1 242.1 245.2 248.2 251.2 254.2 257.1 260.0 262.9 265.7 268.5 271.3

298.2 304.6 310.7 317.5 325.7 333.7 341.5 349.9 359.2 372.2

254.7 258.2 261.6 265.0 268.4 271.7 275.0 278.3 281.5 284.7

176.8 179.2 182.0 185.4 190.1

154.3 156.1 157.9 159.6 161.4

319.4 323.7 328.0 332.0 336.9 341.6 346.8 351.6 356.3 361.2 366.0 372.3 379.0 386.0

295.2 298.8 302.3 305.8 309.3 312.7 316.1 319.5 322.8 326.1 329.4 332.6 335.8 338.9 342.0

a

Standard uncertainty u(p) = 1 kPa, u(T) = 0.1 K. bAll of the expanded uncertainties correspond to a coverage factor of k = 1.96 for a level of confidence of 0.95. cExpanded uncertainty U(Cp, anthracene, cr) = 1.9 J·mol−1·K−1 dExpanded uncertainty U(Cp, pyrene, cr) = 1.8 J·mol−1·K−1 e Expanded uncertainty U(Cp, benzoic acid, cr) = 0.8 J·mol−1·K−1. fExpanded uncertainty U(Cp, 3-hydroxyflavone, cr) = 1.3 J·mol−1·K−1.

Table 4. Heat Capacities of Solid and Gas Phases of the Compounds Studied in Present Work (p = 0.1 MPa)a,b 5-hydroxyflavone T K

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 388.15 393.15 398.15 403.15 408.15 413.15 418.15 423.15 428.15 433.15 438.15 443.15 448.15 453.15 458.15 463.15

Cpm(cr) c

Cpm(g)

6-hydroxyflavone Cpm(cr) d

7-hydroxyflavone

Cpm(g)

Cpm(cr) e

Cpm(g)

6-aminoflavone Cpm(cr) f

Cpm(g)

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

274.6 279.8 285.1 289.4 297.0 302.8 307.0 311.2 312.9 315.9 319.5 323.8 328.8 334.4 338.5 344.8 347.9 350.8 355.6 360.1 365.3 369.6 373.8 377.7 382.3 387.6 395.5

236.3 240.3 244.3 248.2 252.1 256.1 259.9 263.8 267.6 271.4 275.2 279.0 282.7 286.4 290.0 293.6 297.2 300.8 304.3 307.8 311.3 314.7 318.1 321.4 324.7 328.0 331.2 334.4 337.6

244.4 250.3 255.3 260.4 265.7 271.1 277.0 282.6 287.5 292.7 297.3 302.4 307.1 312.4 317.2 321.9 326.7 330.6 335.1 339.8 344.4 348.9 353.2 358.3 362.3 365.8 370.3 373.7 376.9 380.8 383.5 385.7 388.4 391.5 394.2

241.9 245.8 249.8 253.7 257.6 261.4 265.3 269.1 272.9 276.7 280.4 284.1 287.8 291.4 295.0 298.6 302.1 305.6 309.1 312.6 316.0 319.3 322.7 326.0 329.2 332.5 335.7 338.8 342.0 345.0 348.1 351.1 354.1 357.1 360.0

248.1 253.1 259.1 263.4 268.2 272.0 276.8 282.1 286.0 291.4 295.3 299.4 303.6 307.6 312.3 316.2 320.7 324.4 328.2 332.4 336.0 340.1 343.3 347.0 351.4 355.2 358.2 361.9 366.3 369.6 372.3 376.7 379.5 382.7 385.8

241.9 245.9 249.8 253.7 257.6 261.5 265.3 269.2 272.9 276.7 280.4 284.1 287.8 291.5 295.1 298.6 302.2 305.7 309.2 312.6 316.0 319.4 322.7 326.0 329.3 332.5 335.7 338.9 342.0 345.1 348.2 351.2 354.2 357.1 360.0

272.6 277.9 283.4 287.6 292.2 296.7 301.6 306.3 311.1 316.1 320.4 324.5 328.9 333.6 338.1 342.2 346.1 349.8 353.8 358.5 361.8 367.2 371.0 374.6 378.3 381.8 385.4 390.1 395.3 400.4 406.4 411.3 418.5 427.8

247.9 252.0 256.0 260.0 264.0 267.9 271.9 275.8 279.7 283.5 287.3 291.1 294.9 298.6 302.3 305.9 309.6 313.2 316.7 320.2 323.7 327.2 330.6 334.0 337.3 340.6 343.9 347.2 350.4 353.5 356.7 359.8 362.8 365.8 368.8

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Table 4. continued 5-hydroxyflavone T K

Cpm(cr) c J·mol−1·K −1

Cpm(g) J·mol−1·K −1

468.15 473.15 478.15 483.15 488.15 493.15 498.15 503.15 508.15 513.15 518.15 523.15

6-hydroxyflavone Cpm(cr) d

7-hydroxyflavone

Cpm(g)

Cpm(cr) e

6-aminoflavone

Cpm(g)

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

J·mol−1·K −1

397.1 399.2 402.0 404.1 406.1 408.4 412.0

362.8 365.7 368.5 371.3 374.0 376.7 379.4 382.1 384.7 387.3

388.5 390.8 391.9 394.0 398.1 400.9 406.2

362.9 365.7 368.6 371.3 374.1 376.8 379.5 382.1 384.7 387.3 389.9 392.4

Cpm(cr) f

Cpm(g)

J·mol−1·K −1

J·mol−1·K −1

371.8 374.7

a

Standard uncertainty u(p) = 1 kPa, u(T) = 0.1 K. bAll of the expanded uncertainties correspond to a coverage factor of k = 1.96 for a level of confidence of 0.95. cExpanded uncertainty U(Cp, 5-hydroxyflavone, cr) = 1.0 J·mol−1·K−1. dExpanded uncertainty U(Cp, 6-hydroxyflavone, cr) = 1.7 J·mol−1·K−1. eExpanded uncertainty U(Cp, 7-hydroxyflavone, cr) = 2.4 J·mol−1·K−1. fExpanded uncertainty U(Cp, 6-Aminoflavone, cr) = 1.9 J·mol−1·K−1.

Table 5. Heat Capacity Equations of the Solid, Liquid, and Gaseous Phases as Functions of Temperature for All of the Compounds Studied in the Present Work compound anthracene pyrene benzoic acid 3-hydroxyflavone 5-hydroxyflavone 6-hydroxyflavone 7-hydroxyflavone 6-aminoflavone

phase

temperature range/K

equation

correlation coefficient

cr g cr g cr g cr g cr g cr g cr g cr g

293.15−433.15 293.15−433.15 293.15−413.15 293.15−413.15 293.15−388.15 293.15−388.15 293.15−433.15 293.15−438.15 293.15−423.15 293.15−433.15 293.15−498.15 293.15−513.15 293.15−498.15 293.15−523.15 293.15−458.15 293.15−473.15

Cp(anthracene, cr)/J·mol−1·K−1 = −65.804 + 1.003 T/K − 2.683 × 10−4 (T/K)2 Cp(anthracene, g)/J·mol−1·K−1 = −68.040 + 1.007 T/K − 5.165 × 10−4 (T/K)2 Cp(pyrene, cr)/J·mol−1·K−1 = 417.731 − 1.989 T/K + 4.521 × 10−3 (T/K)2 Cp(pyrene, g)/J·mol−1·K−1 = −76.592 + 1.107 T/K − 5.615 × 10−4 (T/K)2 Cp(benzoic acid, cr)/J·mol−1·K−1 = 155.885 − 0.430 T/K + 1.324 × 10−3 (T/K)2 Cp(benzoic acid, g)/ J·mol−1·K−1 = −16.290 + 0.564 T/K − 2.743 × 10−4 (T/K)2 Cp(3-hydroxyflavone, cr)/J·mol−1·K−1 = 319.4 − 0.861 T/K + 2.334 × 10−3 (T/K)2 Cp(3-hydroxyflavone, g)/J·mol−1·K−1 = −52.758 + 1.176 T/K − 6.277 × 10−4 (T/K)2 Cp(5-hydroxyflavone, cr)/J·mol−1·K−1 = 24.434 + 0.848 T/K + 0.501 × 10−4 (T/K)2 Cp(5-hydroxyflavone, g)/J·mol−1·K−1 = −55.953 + 1.180 T/K − 6.264 × 10−4 (T/K)2 Cp(6-hydroxyflavone, cr)/J·mol−1·K−1 = −273.707 + 2.311 T/K − 1.875 × 10−3 (T/K)2 Cp(6-hydroxyflavone, g)/J·mol−1·K−1 = −53.561 + 1.204 T/K − 6.723 × 10−4 (T/K)2 Cp(7-hydroxyflavone, cr)/J·mol−1·K−1 = −141.073 + 1.661 T/K − 1.136 × 10−3 (T/K)2 Cp(7-hydroxyflavone, g)/J·mol−1·K−1 = −53.779 + 1.206 T/K − 6.740 × 10−4 (T/K)2 Cp(6-aminoflavone, cr)/J·mol−1·K−1 = 24.724 + 0.838 T/K + 0.545 × 10−4 (T/K)2 Cp(6-aminoflavone, g)/J·mol−1·K−1 = −52.111 + 1.219 T/K − 6.701 × 10−4 (T/K)2

r2 = 0.9998 r2 = 1.0000 r2 = 0.9992 r2 = 1.0000 r2 = 0.9988 r2 = 1.0000 r2 = 0.9997 r2 = 1.0000 r2 = 0.9975 r2 = 1.0000 r2 = 0.9996 r2 = 1.0000 r2 = 0.9997 r2 = 1.0000 r2 = 0.9976 r2 = 1.0000

g Δcr,1 Hm 1 ⎛ dm ⎞ ln⎜ T ⎟ = B′ − ⎝ dt ⎠ R T

Table 6. Heat Capacities Comparison of the Crystalline Phase and Gas Phase at Constant Pressure at 298.15 K for Anthracene, Pyrene, Benzoic Acid, And Naphthalene against Data Reported in the Literature

(3)

In eq 3, B′ = ln(DMS/R) + c. From eq 3, it follows that plotting ln(dm/dtT) vs 1/T provides a straight line whose slope gives the enthalpy of vaporization or sublimation. Therefore, it is only necessary to accurately measure the rate of mass loss as a function of temperature. For this purpose, TGA Q500 thermogravimetric analysis equipment, from TA Instruments, was used. This equipment has an internal balance with a sensitivity of 0.1 μg and a capacity of 1 g. The sample was placed inside the pan, which was previously exposed to fire for 3 min to remove any dirt. The pan was placed inside the furnace, and the system was closed. After a heat program was entered , during the whole time of the experiment, the mass loss was monitored and quantified over different temperature ranges. The pan was made of platinum with a volume of 0.1 cm3. It was placed inside a furnace that controls the sample atmosphere and

Cpm(cr) J·mol−1·K −1

anthracene

pyrene

benzoic acid

211.7 210.5 207.55 ± 1.27 209.9 ± 1.9a 229.36 229.70 234.86 ± 3.09 225.8 ± 1.8a 146.65 146.79 145.33 145.2 ± 0.8a

ref 60 61 62 this work 64 41 62 this work 65 66 67 this work

Cpm(g) J·mol−1·K −1

ref

184.74 186.4

63 this work

204.2 203.5

62 this work

126.6 127.6

68 this work

a

Expanded uncertainty with a coverage factor k = 1.96 and a confidence level of 0.95. E



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two primary standards and one secondary standard were tested (anthracene, benzoic acid, and pyrene). These compounds have well-known sublimation enthalpies. For determining the enthalpy of sublimation by thermogravimetry under isothermal conditions, the most important parameters to be measured are the amount of mass lost in each isothermal stage, the time of each isothermal stage, and the used temperature range.36 In the experiments for the standards, it was found that an adequate mass loss for each stage must be in the range of 20 μg to 3 mg, which are masses higher than the sensitivity of the TGA Q500 equipment (which is 0.1 μg). It was observed that, within this range of mass loss, the sublimation enthalpies of the standard materials are in accordance with the values recommended in the literature. If the mass loss was below or above the established range, the sublimation enthalpies would be either unreliable or higher (compared to the recommended ones). The isothermal time must include the time required to achieve mass losses in the aforementioned range (20 μg to 30 mg) and the time required by the equipment to achieve the constant temperature. An experimental heating rate of 1 K·min−1 was applied between isotherms, and it was observed that, at this rate, the TGA Q500 requires at least 5 min to reach constant temperature. This time of stabilization should be ignored for the treatment of the data. In all experiments, the analyzed temperature range started before the melting temperature. The temperature ranges selected for the experiments for the standards were 50 K with isothermal stages every 10 K for anthracene and pyrene and 20 K with isothermal stages every 3 K for benzoic acid. These intervals were optimal for reproducing the recommended values. The nitrogen flow used in each experiment was 100 cm3·min−1. In order to test whether different flow rates had an effect on the sublimation enthalpy values, a flow of 160 cm3·min−1 was tested in an anthracene experiment. No significant effect was found. Once the isothermal thermogravimetric method was tested and validated, it was applied to determining the enthalpies of sublimation of a family of hydroxy- and amino-substituted flavones. The experiments were conducted according to the previously established experimental conditions. As in the case of experiments with standard compounds, a temperature range of 50 K was selected below the melting temperature of each flavone, and the mass loss measurements were performed every 10 K within this range. A heating rate of 1 K·min−1

temperature and that allows heating from 298.15 to 1273.15 K at rates of (0.1 to 100) K·min−1. The experimental temperature was measured with a thermocouple with a sensitivity of 0.1 K. The temperature calibration was carried out by determining the Curie temperatures of alumina (425.75 K) and nickel (631.35 K). The balance of the device was calibrated using reference masses of (100 and 1000) mg. In order to optimize the experimental conditions for determining enthalpies of sublimation under isothermal conditions, Table 7. Representative Thermogravimetric Data and Enthalpy of Sublimation for Anthracenea,b T K

(dm/dt )109

(1/T )103

kg·s−1

K −1

ln(dm/dt T)

Anthracene Series 1 383.15 0.1291 2.610 −16.822 393.15 0.2839 2.544 −16.008 403.15 0.5948 2.480 −15.243 413.15 1.1845 2.420 −14.530 423.15 2.2353 2.363 −13.871 433.15 3.9926 2.309 −13.268 series 1 ln(dm/dt T) = 14.1 − 11821.0/T; r2 = 0.9997; σa = 0.3; σb = 108.5; ΔgcrHm(408.15 K)/kJ·mol−1 = 98.3 ± 0.9 series 2 ln(dm/dt T) = 14.4 − 11988.5/T; r2 = 0.9997; σa = 0.3; σb = 104.2; ΔgcrHm(408.15 K)/kJ·mol−1 = 99.7 ± 0.9 series 3 ln(dm/dt T) = 14.1 − 11846.5/T; r2 = 0.9997; σa = 0.3; σb = 109.2; ΔgcrHm(408.15 K)/kJ·mol−1 = 98.5 ± 0.9 series 4 ln(dm/dt T) = 14.3 − 11946.6/T; r2 = 0.9996; σa = 0.3; σb = 114.0; ΔgcrHm(408.15 K)/kJ·mol−1 = 99.3 ± 0.9 series 5 ln(dm/dt T) = 14.2 − 11917.4/T; r2 = 0.9997; σa = 0.3; σb = 107.6; ΔgcrHm(408.15 K)/kJ·mol−1 = 99.1 ± 0.9 weighted average value: ΔgcrHm(anthracene, 408.15 K)/kJ·mol−1 = 99.0 ± 0.9 Pyrene Series series 1 ln(dm/dt T) = 13.3 − 11720.0/T; r2 = 0.9999; σa = 0.2; σb = 71.4; ΔgcrHm(388.15 K)/kJ·mol−1 = 97.4 ± 0.6 series 2 ln(dm/dt T) = 13.3 − 11793.4/T; r2 = 0.9998; σa = 0.2; σb = 85.5; ΔgcrHm(388.15 K)/kJ·mol−1 = 98.1 ± 0.7 series 3 ln(dm/dt T) = 13.2 − 11852.8/T; r2 = 0.9998; σa = 0.2; σb = 86.5; ΔgcrHm(388.15 K)/kJ·mol−1 = 98.5 ± 0.7 series 4 ln(dm/dt T) = 13.2 − 11825.4/T; r2 = 0.9998; σa = 0.2; σb = 83.3; ΔgcrHm(388.15 K)/kJ·mol−1 = 98.3 ± 0.7 series 5 ln(dm/dt T) = 13.1 − 11761.1/T; r2 = 0.9999; σa = 0.2; σb = 71.6; ΔgcrHm(388.15 K)/kJ·mol−1 = 97.8 ± 0.6 weighted average value: ΔgcrHm(pyrene, 388.15 K)/kJ·mol−1 = 98.0 ± 0.7 Benzoic Acid Series series 1 ln(dm/dt T) = 14.2 − 10652.1/T; r2 = 0.9992; σa = 0.3; σb = 113.6; ΔgcrHm(381.15 K)/kJ·mol−1 = 88.6 ± 0.9 series 2 ln(dm/dt T) = 14.3 − 10723.0/T; r2 = 0.9991; σa = 0.3; σb = 119.1; ΔgcrHm(381.15 K)/kJ·mol−1 = 89.2 ± 1.0 series 3 ln(dm/dt T) = 13.8 − 10526.4/T; r2 = 0.9988; σa = 0.4; σb = 138.6; ΔgcrHm(381.15 K)/kJ·mol−1 = 87.5 ± 1.2 series 4 ln(dm/dt T) = 14.1 − 10639.6/T; r2 = 0.9989; σa = 0.3; σb = 133.2; ΔgcrHm(381.15 K)/kJ·mol−1 = 88.5 ± 1.1 series 5 ln(dm/dt T) = 13.8 − 10532.8/T; r2 = 0.9990; σa = 0.3; σb = 126.3; ΔgcrHm(381.15 K)/kJ·mol−1 = 87.6 ± 1.0 weighted average value: ΔgcrHm(benzoic acid, 381.15 K)/kJ·mol−1 = 88.3 ± 1.0 a

Detailed data of the experiments are included in the Supporting Information. bStandard uncertainties u are u(T) = 0.1 K and u(m) = 0.1 μg, and the combined expanded uncertainty Uc is Uc(dm/dt) = 0.066 × 10−9 kg·s−1, Uc(1/T) = 0.001 × 103 K−1, and Uc(ln(dm/dt T) = 0.020 (level of confidence 0.95). The uncertainty for each sublimation enthalpy is the combined standard uncertainty ucomb, where ucomb is a function of the uncertainty of the slope ub, the uncertainty of the temperature uT, and the uncertainty of dm/dt, udm/dt, and is calculated as the positive square root of the sum of the variance of each term. The uncertainty in the slope is computed as σbR × 10−3.

Figure 2. ln(dm/dt T) vs 1/T for the anthracene series (●, ■, ▲, ⧫, −)(blue); the benzoic acid series (●, ■, ▲, ⧫, −)(black); and the pyrene series (●, ■, ▲, ⧫, −)(red). F



Article

between isotherms and a nitrogen flow of 100 cm3·min−1 were applied throughout the experiment. In order to guarantee the absence of any thermal phenomenon of the flavones during the heating in the thermogravimetric equipment, a DSC experiment was carried out at the same rate and over the same temperature range. No strange signal of heat flow was recorded within the detection limits of the equipment. At least four individual experiments were performed per compound, each using a sample mass of (20 to 30) mg. From the experimental data, the mass loss rate is obtained for each isothermal stage and the data are adjusted according to eq 3 and from the slope of the adjustment, the sublimation enthalpy is obtained. To verify that a decomposition process does not take place during the TGA experiments, a sample of the hydroxy- and aminoflavones were condensed at the exit of the sublimation furnace of the TGA equipment and were then analyzed by nuclear magnetic resonance. The observed signals corresponded to the structure of each flavone. The signals associated with each proton and carbon atoms were observed. No additional signal was obtained. The proton and carbon spectra are shown in the Supporting Information.

from at least four experimental measurements, and the associated uncertainty corresponds to the expanded uncertainty with a 0.95 confidence level and a coverage factor of k = 1.96. The data obtained by DSC for anthracene, pyrene, and benzoic acid were compared with the data reported in the literature, and overall agreement was observed for both properties except for anthracene, for which our value is ∼1 kJ·mol−1 higher compared to those reported by other authors. Regarding the flavones, only a few fusion enthalpy values have been reported, and in all cases, our value falls within the range reported by other authors. The heat capacities of the gas phases were obtained from computational calculations by performing molecular geometry optimizations using density functional theory at a B3LYP/ 6-31G(2df,p) level and using the harmonic oscillator approximation, where the vibrational frequencies were scaled by 0.9652 ± 0.0220.58,59 The gas-phase heat capacities were computed over a temperature range from 293.15 K to the melting temperature of each compound. The heat capacity of the crystalline phase was determined through DSC, as described above. The heat capacities for both phases are shown in Tables 3 and 4, and they were fitted to a quadratic equation Cp/J·mol−1·K−1 = a + b(T/K) + c(T/K)2, as shown in Table 5. The heat capacities of the crystalline and gaseous phases at 298.15 K of pyrene, anthracene, and benzoic acid, as obtained here, were compared to those reported in the literature, as shown

■

RESULTS AND DISCUSSION Table 2 shows the fusion temperatures and molar fusion enthalpies obtained by DSC for anthracene, pyrene, benzoic acid, and the flavones studied in this work. The averages were obtained

Table 8. Compilation of Enthalpies of Sublimation for Anthracene, Pyrene, and Benzoic Acida techniqueb

Trange K

anthracene

ME GS C ME CGC-DSC ME ME RV TGA TGA ME PG T ME ME C ME ME RV TGA ME TGA C ME KE C ME SM TGA

340−360 313−363 353−432 339−354 298.15 323.31−367.35 331.27−375.36

98.8 ± 0.4 102.6 99.7 ± 1.5 101.6 ± 4.1 100.8 ± 3.4 100.5 ± 0.3 99.2 ± 0.9

350 338 393 346.5 298.15 345.33 349.27

380.0−400.0 383.15−433.15 322−381 353−393 314−454 348−419 351 348−419 345−369 341−418

98.8 ± 1.2 99.0 ± 1.8c 97.8 ± 3.3 99.31 ± 0.9 97.9 97.47 ± 0.70 100.1 ± 1.7 97.68 ± 0.3 98.3 ± 0.6 103.25 ± 2.05

390.0 408.15 352 373 433 384 351 384 356 379.5

363.15−413.15 307−314 338.0−358.0 321 293−313 291−307 298

98.0 ± 1.4c 88.7 ± 1.7 90.2 ± 1.9 87.75 ± 0.60 90.35 ± 0.25 90.89 89.50 ± 0.34

372.15−393.15

88.3 ± 2.0c

488.15 310.5 348.0 321 303 299 298 298.15 298.15 381.15

pyrene

benzoic acid

a

g Δcr Hm(Tav ) kJ·mol−1

compound

Tav K

T

m ΔCpdT ∫298.15 K

−3.5 ± 1.5d

−3.0 ± 1.6d

−1.6 ± 0.9d

g Δcr Hm(298.15 K) kJ·mol−1

100.2 ± 0.4 103.9 ± 2.7 102.7 ± 1.8 103.15 ± 4.4 100.8 ± 3.4 101.8 ± 0.3 100.6 ± 0.9 101.9 ± 1.3 101.8 ± 2.4 102.5 ± 2.3e 99.7 ± 3.4 102.3 ± 1.5 100.74 ± 2.84 100.34 ± 2.0 101.9 ± 1.8 100.55 ± 1.9 100.1 ± 0.6 104.46 100.3 ± 1.0 101.0 ± 2.1e 89.25 ± 1.7 91.3 ± 3.7 88.90 ± 0.60 90.6 ± 0.4 90.91 89.50 ± 0.34 93.3 ± 1.2 91.4 ± 0.5 89.9 ± 2.2e

ref 71 72 73 74 75 76 76 40 20 this work 77 78 79 80 81 80 82 83 40 this work 84 20 85 86 87 88 89 90 this work

b

Standard uncertainty u(T) = 0.1 K. Techniques: ME, method of effusion; GS, gas saturation transpiration; DC, drop calorimetry; C, calorimetry; PG, pressure gauge; DSC, differential scanning calorimetry; T, transpiration; TGA, thermogravimetry; CGC, correlation of gas chromatography; RV, recommended value; and SM, static method. cThe uncertainty is the expanded uncertainty U for a confidence level for a coverage factor of k = 1.96 and a confidence level of 0.95. dExpanded uncertainty for a confidence level for a coverage factor of k = 1.96 and a confidence level of 0.95, which was calculated from the uncertainty of the heat capacity of the crystalline and gaseous phases. eThe uncertainty was calculated by applying the root method of the sum of the squares of the uncertainty of the enthalpy of sublimation at Tav and the uncertainty of the integral of the heat capacities. G



Article

Table 9. Representative ThermogravImetric Data and Enthalpy of Sublimation for Flavonesa,b T K

(dm/dt )109 kg·s−1

(1/T )103 K −1

T K

ln(dm/dt T)

3-Hydroxyflavone Series 1 393.15 0.0188 2.544 −18.724 403.15 0.0458 2.480 −17.807 413.15 0.1029 2.420 −16.974 423.15 0.2221 2.363 −16.180 433.15 0.4617 2.309 −15.425 series 1 ln(dm/dt T) = 16.9 − 14015.6/T; r2 = 0.9999; σa = 0.2; σb = 80.7; ΔgcrHm(413.15 K)/kJ·mol−1 = 116.5 ± 0.7 series 2 ln(dm/dt T) = 17.1 − 13951.8/T; r2 = 0.9998; σa = 0.3; σb = 103.9; ΔgcrHm(413.15 K)/kJ·mol−1 = 116.0 ± 0.9 series 3 ln(dm/dt T) = 16.6 − 13730.7/T; r2 = 0.9988; σa = 0.7; σb = 279.7; ΔgcrHm(413.15 K)/kJ·mol−1 = 114.2 ± 2.3 series 4 ln(dm/dt T) = 17.2 − 13994.4/T; r2 = 0.9999; σa = 0.1; σb = 61.0; ΔgcrHm(413.15 K)/kJ·mol−1 = 116.3 ± 0.5 weighted average value: ΔgcrHm(3-hydroxyflavone, 413.15 K)/kJ·mol−1 = 116.3 ± 0.7 5-Hydroxyflavone series 1 ln(dm/dt T) = 16.7 − 13719.6/T; r2=0.9997; σa = 0.3; σb = 137.6; −1 g ΔcrHm(403.15 K)/kJ·mol = 114.1 ± 1.1 series 2 ln(dm/dt T)=15.4 − 13364.5/T; r2=0.9993; σa = 0.5; σb = 202.1; ΔgcrHm(403.15 K)/kJ·mol−1 = 111.1 ± 1.7 series 3 ln(dm/dt T)=16.6 − 13811.2/T; r2=0.9994; σa = 0.5; σb = 201.1; ΔgcrHm(403.15 K)/kJ·mol−1 = 114.8 ± 1.7 series 4 ln(dm/dt T)=15.9 − 13534.3/T; r2=0.9999; σa = 0.2; σb = 92.2; ΔgcrHm(403.15 K)/kJ·mol−1 = 112.5 ± 0.8 weighted average value: ΔgcrHm(5-hydroxyflavone, 403.15 K)/kJ·mol−1 = 113.0 ± 1.1

(dm/dt )109 kg·s−1

(1/T )103 K −1

ln(dm/dt T)

6-Hydroxyflavone series 1 ln(dm/dt T) = 20.1 − 17861.4/T; r2 = 0.9999; σa = 0.1; σb = 46.7; ΔgcrHm(478.15 K)/kJ·mol−1 = 148.5 ± 0.4 series 2 ln(dm/dt T) = 20.2 − 17905.5/T; r2 = 0.9995; σa = 0.4; σb = 208.2; ΔgcrHm(478.15 K)/kJ·mol−1 = 148.9 ± 1.7 series 3 ln(dm/dt T) = 20.2 − 17912.4/T; r2 = 0.9998; σa = 0.2; σb = 101.3; ΔgcrHm(478.15 K)/kJ·mol−1 = 148.9 ± 0.8 series 4 ln(dm/dt T) = 20.0 − 17783.2/T; r2 = 0.9999; σa = 0.1; σb = 33.8; ΔgcrHm(478.15 K)/kJ·mol−1 = 147.8 ± 0.3 weighted average value: ΔgcrHm(6-hydroxyflavone, 478.15 K)/kJ·mol−1 = 148.1 ± 0.5 7-Hydroxyflavone series 1 ln(dm/dt T) = 20.3 − 18290.7/T; r2 = 0.9993; σa = 0.5; σb = 239.6; ΔgcrHm(473.15 K)/kJ·mol−1 = 152.1 ± 2.0 series 2 ln(dm/dt T) = 20.6 − 18448.6/T; r2 = 0.9999; σa = 0.2; σb = 112.4; ΔgcrHm(473.15 K)/kJ·mol−1 = 153.4 ± 0.9 series 3 ln(dm/dt T) = 21.3 − 18749.6/T; r2 = 0.9999; σa = 0.2; σb = 72.4; ΔgcrHm(473.15 K)/kJ·mol−1 = 155.9 ± 0.6 series 4 ln(dm/dt T) = 20.2 − 18275.9/T; r2 = 0.9997; σa = 0.4; σb = 170.7; ΔgcrHm(473.15 K)/kJ·mol−1 = 151.9 ± 1.4 weighted average value: ΔgcrHm(7-hydroxyflavone, 473.15 K)/kJ·mol−1 = 154.6 ± 0.9 6-Aminoflavone series 1 ln(dm/dt T) = 20.0 − 17216.1/T; r2 = 0.9999; σa = 0.1; σb = 34.6; ΔgcrHm(452.15 K)/kJ·mol−1 = 143.1 ± 0.3 series 2 ln(dm/dt T) = 20.1 − 17221.2/T; r2 = 0.9999; σa = 0.1; σb = 62.3; ΔgcrHm(452.15 K)/kJ·mol−1 = 143.2 ± 0.5 series 3 ln(dm/dt T) = 19.8 − 17.1190/T; r2 = 0.9998; σa = 0.3; σb = 144.2; ΔgcrHm(452.15 K)/kJ·mol−1 = 142.3 ± 1.2 series 4 ln(dm/dt T) = 20.1 − 17302.9/T; r2 = 0.9999; σa = 0.1; σb = 51.1; ΔgcrHm(452.15 K)/kJ·mol−1 = 143.9 ± 0.4 weighted average value: ΔgcrHm(6-aminoflavone, 452.15 K)/kJ·mol−1 = 143.3 ± 0.4

a Detailed data of the experiments are included in the Supporting Information. bStandard uncertainties u are u(T) = 0.1 K and u(m) = 0.1 μg, and the combined expanded uncertainty Uc is Uc(dm/dt) = 0.066 × 10−9 kg·s−1, Uc(1/T) = 0.001 × 103 K−1, and Uc(ln(dm/dtT) = 0.020 (level of confidence 0.95). The uncertainty for each sublimation enthalpy is the combined standard uncertainty ucomb, where ucomb is a function of the uncertainty of the slope ub, the uncertainty of the temperature uT, and the uncertainty of dm/dt, udm/dt, and is calculated as the positive square root of the sum of the variance of each term. The uncertainty of the slope is computed as σbR × 10−3.

where xi represents the enthalpy of sublimation and u2comb,i is the respective standard combined uncertainty.70 The complete data set for the reference compounds is shown in the Supporting Information. Linear regression ln(dm/dt T) vs 1/T of the whole experimental series of anthracene, benzoic acid, and pyrene is shown in Figure 2. In order to calculate the sublimation enthalpies at 298.15 K, it was necessary to calculate values of the heat capacity of the crystalline phase and of the gas phase, as shown in the Kirchhoff equation (eq 4).

in Table 6. Both the heat capacities of the crystalline phase (obtained by experimental methods) and the heat capacities of the gas phase (obtained by computational methods) are in good agreement. In the solid phase, the greatest difference was observed for pyrene. Our value differs by (3.56 and 3.90) J·mol−1·K−1 relative to the values reported by Smith et al.64 and Wong et al.,41 respectively. In the gas phase, the largest difference was observed for anthracene, and our value differs by 1.66 J·mol−1·K−1 compared to that reported by Dorofeeva.63 In Table 7, representative values of an experimental series of anthracene are shown. According to eq 3, the plot ln(dm/dt T) versus 1/T produces a straight line from whose slope the enthalpy of sublimation was calculated. The results of five experiments that were performed for each reference material are also shown in Table 7. For each experimental series, the correlation coefficient r2, uncertainty of intersection σa, and slope uncertainty σb were calculated. The enthalpy of sublimation corresponds to the average temperature (Tav) of the analyzed temperature range. The uncertainty associated with each measurement corresponds to the combined standard uncertainty, ucomb, and was calculated by taking into account the uncertainties stemming from the slope of ln(dm/dt T)69 Because the enthalpy value of sublimation has its own associated uncertainty, weighted average μ was obtained, which was calculated as μ = Σ(xi/u2comb,i)/Σ(1/u2comb,i). The uncertainty associated with this weighted average was calculated as ucomb = (N/Σ(1/u2comb,i))1/2,

Δcrg Hm(298.15K) = Δcrg Hm(Tav) −

Tav

∫298.15K ΔCpm dT

(4)

Here, ΔCpm = Cpm(g) − Cpm(cr). Table 8 shows the enthalpies of sublimation at the experimental average temperature Tav, the values of the integral ∫ Tav 298.15 KΔCp dT, and the enthalpies of sublimation at 298.15 K, which were calculated using eq 4. The uncertainty in the enthalpy of sublimation at Tav corresponds to the expanded one for a confidence level of 0.95 and a coverage factor of k = 1.96. The uncertainty in the integral of the heat capacity was calculated from the uncertainty in the heat capacity of the crystalline and gaseous phases. The uncertainty in the enthalpy of sublimation at T = 298.15 K was calculated by applying the root method of the sum of the squares of the uncertainty in the enthalpy of sublimation at Tav and the uncertainty in the integral of the heat H



Article

experimental series, where the uncertainty associated with each series and the weighted average was calculated as in Table 7. The linear regression of all of the experimental series for the hydroxyflavones and the aminoflavone is shown in Figure 3. The calculation of the enthalpy of sublimation at 298.15 K was performed using eq 4, and the heat capacities of the solid and gaseous phases were taken from Table 5. Table 10 shows the sublimation enthalpies at the average experimental temperature, the values of the integral ∫ Tav 298.15 K ΔCp dT, and the sublimation enthalpies at 298.15 K. According to the data shown in Table 10, the difference in the enthalpy of sublimation at 298.15 between 3-hydroxyflavone and 5-hydroxyflavone is (1.2 ± 3.6) kJ·mol−1. This indicates that in the 3-hydroxyflavone the intermolecular interactions in the crystalline phase are only slightly stronger than they are in the 5-hydroxyflavone. This can be attributed to the fact that at these positions the carbonyl group is relatively close to the −OH group, which causes interactions with neighboring molecules of the same order of magnitude. When the OH group is located at positions 6 and 7, the enthalpy of sublimation increases considerably, implying that this group causes stronger intermolecular interactions with respect to the other isomers. 7-Hydroxyflavone has the highest enthalpy value of sublimation of all of the studied isomers. If the sublimation enthalpies of 6-hydroxyflavone and 6-aminoflavone are compared, a difference of just (3.6 ± 2.8) kJ·mol−1 is observed, which indicates that the presence of a substituent at position 6 of the flavone causes similar intermolecular interactions. Sousa et al.30 recently reported the sublimation enthalpy for flavone as 108.2 ± 1.7 kJ mol−1, which is lower than the values for flavones studied in this work because flavone does not have any amino or hydroxy groups with which it can form some intermolecular interaction by a hydrogen bridge with neighboring molecules.

capacity. Table 8 also shows the comparison of our values against those obtained by other techniques and reported in the literature. The enthalpy of sublimation at 298.15 K for anthracene obtained in this work is in agreement with those reported by Malaspina et al.,73 Santos et al.,76 and Ramos et al.,20 whose values were obtained by calorimetry, the effusion method, and thermogravimetry, respectively. The difference from the recommended value by Roux et al. is 0.6 kJ·mol−1. The most notable difference is 1.4 kJ·mol−1 according to the reported value by Hansen et al.72 The values reported for pyrene are within the uncertainty of the value reported in the present work. The largest difference is 3.46 kJ·mol−1 with respect to the value reported by Siddiqi et al.,83 which was obtained by the effusion method. The difference with the recommended value by Roux et al.40 is 0.7 kJ·mol−1. Finally, all values for benzoic acid reported in Table 8 are within the uncertainty of the value obtained in this work. The largest difference is 1.4 kJ·mol−1 according to a value obtained by TGA in dynamic mode.20 According to the data presented in Table 8, in this work we have been able to reproduce enthalpy values of sublimation reported in the literature for the reference materials, two primary (benzoic acid and anthracene) and one secondary (pyrene), with an accuracy of ±2.2 kJ·mol−1. The reliability of isothermal thermogravimetry for the determination of sublimation enthalpies is proved above. Once the isothermal thermogravimetry was tested through the standards, this technique was applied to study hydroxyflavones and an aminoflavone. Table 9 shows the data of a thermogravimetric experiment on them and the result of the linear adjustment according to eq 3, from whose slope the enthalpy of sublimation is derived. The same table shows the result of four

■

CONCLUSIONS The sublimation enthalpy results for anthracene, pyrene, and benzoic acid show that the application of thermogravimetry in isothermal mode is a reliable indirect technique for obtaining this physical property. The values obtained in this work are in good agreement with the values reported in the literature. Uncertainties on the order of ±2.2 kJ·mol−1 were obtained, which are similar to those obtained by direct calorimetric methods and some indirect methods. Isothermal thermogravimetry was applied to study a family of flavones. The data showed that the flavones with the −OH group at positions 6 and 7 have the highest sublimation enthalpies compared to the 3-hydroxy and 5-hydroxyflavone isomers.

Figure 3. ln(dm/dtT) vs 1/T for the 3-hydroxyflavone series (●, ■, ▲, ⧫)(blue); the 5-hydroxyflavone series (●, ■, ▲, ⧫)(dark green); the 6-hydroxyflavone series (●, ■, ▲, ⧫)(bright green); the 7-hydroxyflavone series (●, ■, ▲, ⧫)(black); and the 6-aminoflavone series (●, ■, ▲, ⧫)(yellow).

Table 10. Enthalpies of Sublimation for Hydroxy and Amino Flavones Studied in This Worka compound 3-hydroxyflavone 5-hydroxyflavone 6-hydroxyflavone 7-hydroxyflavone 6-aminoflavone

Trange K

383.15−433.15 383.15−423.15 453.15−503.15 448.15−498.15 436.15−468.15

g Δcr Hm(Tav ) b

Tav K

kJ·mol−1

116.3 ± 1.4 113.0 ± 2.2 148.1 ± 1.0 154.6 ± 1.8 143.3 ± 0.8

413.15 403.15 478.15 473.15 452.15

T av

∫298.15 K ΔCp dT c −2.9 ± 1.7 −5.0 ± 1.7 −4.5 ± 1.7 −3.2 ± 1.7 −5.7 ± 1.8

g Δcr Hm(298·15 K) d

kJ·mol−1

119.2 ± 2.2 118.0 ± 2.8 152.6 ± 2.0 157.8 ± 2.5 149.0 ± 2.0

a

Standard uncertainty u(T) = 0.1 K. bThe uncertainty is the expanded uncertainty U for a confidence level for a coverage factor of k = 1.96 and a confidence level of 0.95. cExpanded uncertainty for a confidence level for a coverage factor of k = 1.96 and a confidence level of 0.95, which was calculated from the uncertainty of the heat capacity of the crystalline and gaseous phases. dThe uncertainty was calculated by applying the root method of the sum of the squares of the uncertainty of the enthalpy of sublimation at Tav and the uncertainty of the integral of the heat capacities. I



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7-Hydroxyflavone has the highest enthalpy of sublimation of the series of compounds studied.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b01034. The complete data set for the DSC experiments of anthracene, benzoic acid, pyrene, and hydroxy- and aminoflavones are shown in Table S1. Complete data series of the thermogravimetric experiments that were used to derive the sublimation enthalpy of all of the compounds studied in this work are shown in Tables S2−S9. The 1H NMR and 13C NMR spectra of flavones are shown in Figures S1−S9. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel: +52 222 2295500x7532. Fax: +52 222 2295584. E-mail: [email protected]. ORCID

Henoc Flores: 0000-0003-3661-9684 Elsa A. Camarillo: 0000-0001-8922-2344 Rafael Notario: 0000-0003-2957-8183 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank VIEP-BUAP for financial support through project CAJE-NAT17-1 and CONACYT for financial aid to purchase equipment (INFRA 2015, 0254854). F.R., O.S,. and G.P. thank CONACYT México for their grants (registration numbers 268314, 595216, and 321454, respectively). The authors thank J.M. Solano-Altamirano for his revisions and useful suggestions on the manuscript. The authors thank A.K. Girón for the analysis of the NMR spectra.

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REFERENCES

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Isothermal Thermogravimetric Study for Determining Sublimation

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